Problem: Find the greatest common factor of $26$ and $14$.
Solution: The greatest common factor (GCF) is the largest number that is a factor of both $26$ and $14$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}26 &=2\cdot13\\\\\\\\ 14&=2\cdot7 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}26 &=2\cdot13\\\\\\\\ 14&=2\cdot7 \end{aligned}$ Each number shares the factor ${2}$, so the GCF is ${2}$. The greatest common factor of $26$ and $14$ is $2$.